where the limit is for \(m\)  tending to \(x\)  \(p\) -adically in \(\mathbb {Z}_{\ge 0}\) .
In 2015, Swisher [1]} proved the following unified form of
van Hamme's three supercongruences in (REF ):
\(\sum _{k=0}^{a(b p-1)}(-1)^{k}\left(\frac{2 k}{a}+1\right) \frac{(a)_{k}^{3}}{k !^{3}}\equiv (-1)^{a(b p-1)} p \cdot b=\frac{-p b}{\Gamma _{p}(a) \Gamma _{p}(1-a)} \pmod {p^3},\) 
